IMO 1991 Problem 2

Let $n > 6\,$ be an integer and $a_{1},a_{2},\cdots ,a_{k}\,$ be all the natural numbers less than $n$ and relatively prime to $n$ . If $$a_{2} - a_{1} = a_{3} - a_{2} = \cdots = a_{k} - a_{k - 1} > 0,$$ prove that $n\,$ must be either a prime number or a power of $2$ .